Transmission Of Heat Question 270

Question: A black body has maximum wavelength $ {\lambda _{m}} $ at temperature 2000 K. Its corresponding wavelength at temperature 3000 K will be

[CBSE PMT 2001; Kerala PET 2005]

Options:

A) $ \frac{3}{2}{\lambda _{m}} $

B) $ \frac{2}{3}{\lambda _{m}} $

C) $ \frac{4}{9}{\lambda _{m}} $

D) $ \frac{9}{4}{\lambda _{m}} $

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Answer:

Correct Answer: B

Solution:

$ {\lambda _{m _{2}}}=\frac{T _{1}}{T _{2}}\times {\lambda _{m _{1}}} $

$ =\frac{2000}{3000}\times {\lambda _{m _{1}}}=\frac{2}{3}{\lambda _{m _{1}}}=\frac{2}{3}{\lambda _{m}} $